WFD Saturation Issues

Abstract

This memo addresses the problems of capacitive overshoot of PMT
signals introduced at the PMT signal fanout and the capactive
undershoot which originates in the WFD daughter card discriminator
circuitry. These AC-coupling effects can cause the WFD to record more
data than our readout window allows. This memo describes the effect
and proposes a solution requiring a simple modification of the RC time
constant of the input to the WFD daughter card discriminators.

Description of the Problem

The PMT signal is AC coupled through a 2.2 uF capacitor in the output
of the B.U. Fanout. This eliminates D.C. offset from the high speed
buffer amplifiers. For most fast pulses, the effect is simply to force
the baseline to 0V with respect to system ground. However, for large
enough pulses (or high enough rates- not an issue for us), the
capacitor charges up, and then discharges through 50 Ohms, with a time
constant of approximately 100 usec. This distorts the shape of the
output pulse, as seen in figure 2. The first deleterious effect is
that for large negative pulses, a positive overshoot is induced which
can keep the positive threshold of the +-2.5 mV WFD threshold on. This
reduces the level of zero-suppression and causes the initial waveform
data (the data of interest) to fall outside our limited storage
window. This effect has been seen for some time, mostly in large
showering events. But it was recently recognized by Doug Michael
and Sophia Kyriazopolou, from bright LED calibration data, that we
also would lose some range of monopole sensitivity.

Figure 1. A
copy of each input signal is passed to a circuit like this one. The
diode is to help reduce crosstalk for large negative pulses. The
proposed fix in this memo is to reduce the net capacitance of C115 and
C116.

Figure 2. The output of
the fanout in response to a -2.2V by 30 microsecond square wave
input. The positive overshoot coming out of the PMT fanout is clearly
visible. The time constant for its decay is approximately 100usec,
long enough to fill our current WFD buffer maximum of 40
kilobytes. 40 kilobytes corresponds to 20 kilosamples, or equivalently
100 microseconds of time.

We considered disconnecting the positive discriminator from the WFD
daughter card, but that lead Iaonnis and Erik Katsavounidis to
recognize a second, related problem. If one takes the output from the
fanout (figure 2) and passes it through the discriminator
preamplifier, a second stage of capacitive coupling can cause a
negative undershoot, shown in Figure 3. Even if the positive threshold
is eliminated, the negative undershoot can again trigger the -2.5 mV
threshold and force excess data to be recorded that causes the WFD to
lose the initial pulse.

Figure 3. The
input to the discriminator for the signal shown in figure 2. The
positive overshoot is distorted before input to the discriminators so that
it falls below ground and discharges with a very long time constant of
about 400 microseconds.

These curves were made using square wave signals generated by an
Hewlett-Packard pulser with programmable amplitudes between -0.090V
and -7.20V, and pulse widths between 300ns and 30usec. The frequency
of the pulses was set to 1Hz to reduce the level of noise on the
baseline and to eliminate the chance of one pulse affecting subsequent
pulses. The rise and fall times of the pulses were set to 100ns.
Faster risetimes were possible, but contributed additional overshoot
from the pulser itself.

The pulses were fed through a standard MACRO PMT fanout to a WFD
daughter card mounted on a custom built test station. The daughter card
test station provides all of the necessary operating voltages to one or
two daughter cards, and allows a single threshold to be programmed on
all inputs. This threshold was set to 6mV as measured by a Fluke DVM at
J3 pin 3 of the daughter card.

A Proposed Fix

Bill Earle, project engineer for the WFD electronics,
suggested that we decrease the capacitance in the RC filter at the
discriminator input. The capacitor's only function is to eliminate DC
offset from the 3:1 amplifier that would affect our ability to
discriminate on single photoelectron signals. Decreasing its value
would not impede this function. (ETK and IK also discussed solutions along
these lines after the Frascati meeting, before the negative undershoot
problem had been identified).

Changing this capacitor has non-intuitive implications. Our goal
is to eliminate the long pulses that saturate the WFD without
eliminating real monopole data. Ideally, one would work with
undistorted pulses at all times, and the discriminator pulses would
ideally match when the input pulse is under or over threshold. By
reducing the capacitance, we cause deliberate sharp positive and
negative overshoots that control the discriminator data. Reducing the
time constant of the RC filter too low will also limit the data from
long monopole pulses. The time constant sets an upper limit on the
maximum digitizable signal width. Figure 4 illustrates a case where a
large, long pulse has data lost after recording the beginning of the
pulse. While losing any data is not ideal, it is important to
realize that with this scheme we would still record the beginning of a
wide monopole pulse and catch the exit time from the trailing edge,
providing adequate information for making a beta calculation.

Figure 4. The same pulse shown above is passed through a modified
input with C115 removed and C116 changed to .01uF, resulting in a total
capacitance a factor of hundred below its current value of 1uF and a time
constant of about 1.2usec. For wide pulses like this 30usec
pulse, the signal will not trigger either the positive or negative
discriminators after the signal has decayed below threshold, but that
the trailing edge of the pulse will trigger. For a monopole of this
width we would expect single photoelectrons and not a -2V Pulse.
Unphysical pulse parameters were chosen to amplify the data loss for clarity.

Another important factor in our favor is that real monopole pulses
will have more high frequency structure than our square wave test
pulses due to PMT fluctuations. To some degree, the RC filter will
retrigger on the higher-frequency PMT fluctuations in real monopole
pulses, reducing the time of lost data. However, the voltage-limiting
diode at D110 will suppress this for pulse heights below approximately
-380mV. We hope to quantify this effect through PSPICE simulations in
the near future.

Tests at C=1uF, .1uf, .05uF, and .01uF

CMO modified the value of the capacitance at three of the four
inputs of one daughter card. Input one was unmodifed, C=.1uF was
installed on input two, C=.01uF on input three, and C=.05uF was
installed on input four. No other modifications were made. The
positive discriminator was left intact on all four inputs. Following
similar tests made at LNGS by Iaonnis and Erik, he measured the
critical pulse height for several different pulse widths, finding the
maximum voltage at each width where the total discriminated width
reached 100usec. This is the point where the WFD will start to lose
the original signal. The data for unmodified channels is shown in
Table 1, and for modified channels in Table 2.

Table 1. For each pulse width, the critical pulse height in Volts is
found where capacitive effects cause a total of 100usec of
discriminator time. The critical values for widths from 8 to 30 usec
was not determined because the input pulse size could not easily be
set to less that 90 mV.

Table 2. For each pulse width, the critical pulse height in
Volts is found where capacitive effects cause a total of 100usec of
discriminator time. Critical values in excess of 7.2V amplitude were
not determined because the input pulse size could not easily be set to
greater than 7.2V.

Results

By comparing the data to the signal expected for monopoles and
dyons we can gauge the best choice for C. In Figure 5, we assume that
a typical muon is a 2V, 75ns wide triangular signal and that the
charge derived from the integrated pulse at the PMT fanout scales with
light yield. To compute beta we assume a pathlength of 20cm.

Figure 5. This figure compares the critical pulse height as a
function of pulse width versus the dL/dX curves for dyons and
monopoles. For a 20 cm path length, our current configuration (1uF,
marked in blue) is fully efficient for monopoles up to at least
beta=3E-3. We are insensitive to a larger region for dyons. The
proposed fix is marked by the black curve labelled .01uF.

The figure suggests that for these given assumptions we are
completely sensitive to bare monopoles for beta less than 3x10^-3 at
least down to beta of 2E-4. Below this point we have insufficient
data due to the minimum allowed pulse from our HP pulser. However
the expected signal below beta of 2E-4 will approach the single
photoelectron trains that we already know we are sensitive to.
Above beta=3E-3, the curves possibly cross at some point out of reach of our
measurement, but at a pulse height no greater than 10V where our
horizontal PMT pairs saturate.

Our effective sensitivity for a more conservative pathlength choice
of 50 cm is shown in Figure 6. From acceptance Monte Carlo, we
estimate that for an isotropic distribution, 93 per cent of all tracks
will cross scintillator tanks in less than 50 cm. In this worst case
estimate geometry, the capacitive effects could cause us to lose
monopoles of beta greater than 4E-4.

Figure 6. This figure compares the critical pulse height as a
function of pulse width versus the dL/dX curves for dyons and
monopoles assuming a 50 cm path length.

Decreasing the capacitor to C=.1uF and C=.05uF at the
discriminator to input restores our sensitivity for monopoles,
but to be sensitive for dyons we would have to drop this near C=.01uF.
This is an appealing choice, because it simplifies the daughtercard
modifications; one would simply remove the 1uF capacitor at D115.

However, the trade-off is shown in Figure 7. For small values of C
the WFD may not digitize the entire signal because the same RC circuit
that dampens the positive and negative overshoots will also cutoff the
recording signal. This effect is quantified in Figure 7 for the
critical pulse height. For C=.01uF there is significant cutoff below
beta=1E-4, but only for unexpectedly large amplitude (the critical
pulse height at beta=2E-5 is 1.5V). This effect would not be seen at
low light levels, where photelectron trains continuously retrigger the
discriminator. Quantitative estimates in this region remain to be
made.

Figure
7. For a given RC decay time there is an upper limit on the pulse
width of an input pulse that will completely trigger the WFD
discriminator. This upper limit is a function of both the input pulse
width and amplitude. Shown is the minimum pulse amplitude for a given
width so that the WFD discriminates on the entire pulse. For
unmodified daughter cards (C=1uF, not shown) the effect is not
present. For C=.1uF and C=.05uF (shown above) the effect turns on in
a region where the actual exected monopole and dyon signal are single
photoelectron chains. For C=.01uF there will be data loss for
monopoles with beta 3E-4 and 5E-4 and for dyons with beta
between 1E-4 and 2E-4. This plot assume a path length of 50cm.

Conclusions

By reducing the time constant at the input to the WFD daughter card
discriminator we can improve our sensitivity to monopoles and dyons by
forcing the WFD to stop digitizing on long positive overshoot. There
is a very simple fix, involving only removing 4 capacitors on each
daughter card. Note that this mechanism requires that we do not
remove the positive discriminators from the discriminator circuit,
which would have been accomplished through a tricky lifting of surface
mount pins.

We are still studying a side-effect where the reduced time constant
also causes the WFD to prematurely stop digitizing some slow, high
pulses. We would still see a distinctive signature, with data from the
beginning of the pulse and the trailing edge. Photoelectron
fluctuations are likely to help fill in the missing data.

Before making this modification on all MACRO WFD channels, we
should modify a few and analyze both normal MACRO data and pulser
data. We will also simulate the fanout plus frontend circuit using
PSPICE to better estimate realistic monopole waveforms than pulsers or
LEDs can provide.